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\title{Management Strategy Evaluation Framework for North Atlantic Albacore}

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\author{Gorka Merino           \footnote{{AZTI-Tecnalia, Herrera Kaia Portualdea, 20110, Pasaia, Spain; ~gmerino@azti.es; ~Phone: +34 667 174 456 ~Fax: +34 94 657 25 55.}}, 
        Paul De Bruyn         		\footnote{{ICCAT Secretariat, C/Coraz\'{o}n de Mar\'{\i}a, 8. 28002 Madrid, Spain; ~Laurie.Kell@iccat.int; ~Phone: +34 914 165 600 ~Fax: +34 914 152 612.}},
        Haritz Arrizabalaga    \footnotemark[2],
        Josetxu Ortiz de Urbina\footnote{{Instituto Espa\~nol de Oceanograf\'{\i}a IEO- CO M\'{a}laga, Pto. Pesquero s/n, 29640 Fuengirola (M\'{a}laga), Spain; ~urbina@ma.ieo.es; ~Phone: +34 952 19 71 24 ~Fax: +34 952 46 38 08.}}, \\
        Laurence T. Kell       \footnotemark[3]
        }

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\begin{abstract}
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\begin{keyword}
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%% or \MSC[2008] code \sep code (2000 is the default)
Management Strategy Evaluation, Precautionary Approach, Risk, tuna RFMOs, ICCATm Atlantic, Uncertainty, Albacore, \textit{Thunnus alalunga} 

\end{keyword}

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\newpage
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%% main text

\section{Introduction}\label{intro}

In this paper we describe an \gls{MSE} framework for North Atlantic \gls{alb}. We do not conduct an \gls{MSE}, 
as the intention is to provide a reference document that details the specifications of the \gls{OM}, \gls{oem} and\gls{MP} that 
will be used in subsequent studies. 	


\section{Material and Methods}\label{mm}

\gls{MSE} involves a number of steps, after \cite{punt2007developing}, i.e.

\begin{description}
 \item[Objectives] Identification of management objectives and performance measures to quantify the extent to which goals have been achieved.
 \item[Scenarios] Selection of hypotheses and the development of Operating Models (i.e. simulation models) scenarios representing those hypotheses.
 \item[Management Strategies] Identification of candidate management options and coding these up as Management Procedures (i.e.the combination of pre-defined 
       data, together with an algorithm to which such data are input to set control measures).
 \item[Conditioning] Developing Operating Model based on data and knowledge and possible rejection and weighting of hypotheses.
 \item[Simulation] Running the \gls{MSE} in order to evaluate of the performance of the Management Strategies by projecting the Operating Model forward using the Management Procedures
 \item[Adopting] i.e. choosing the Management Strategy that best meets management objectives.
\end{description}

In this paper we only consider the first four steps, i.e. identifying performance measures, specifying OM, OEM and MP scenarios and the methodology
to be used for conditioning.

There are various ways to condition an \gls{OM}, which generally requires the use of the available data and knowledge
(and possible rejection of hypotheses [or combinations of hypotheses] which are not compatible with those data and knowledge). 
There are various ways to construct operating models \cite{kell2006operational}. In this case the \gls{OM} is the currently-used 
stock assessment model, i.e. \gls{multifan-cl} to ensure continuity of advice and transparency to working group members.
However simulation test using \gls{multifan-cl} as part of an MP would be computationally intensive we therefore use a simpler stock assessment model 
for the MP i.e a biomass dynamic model. 

The use of the assessment model as the operating 
model may appear to imply that the assessment model describe nature almost perfectly. However, by using scenarios based on
alternative hypotheses and data sets the uncertainties in the stock and fleet dynamics can be addressed.
Conditioning the \gls{OM} required setting up appropraite input files and then running \gls{multifan-cl} to convergence (see SCRS-2013-34 and SCRS-2013-58).

The data used are the input data sets from the 2013 stock assessment of \gls{alb} using \gls{multifan-cl}, \cite{fournier1998multifan}. 


Choice of scenarios are based on a factorial design.  A full factorial experiment is one whose 
design consists of two or more factors, each with discrete possible values or \textit{levels}, and where experimental 
units take on all possible combinations of these levels across all factors. Such a design is better able to
represents the complexity of the real world and allows an evaluation of whether the effect of one factor
depends on the level of another factor. The potentially large number of combinations in a full factorial design 
may mean that it is not possible to run them all in the time available in a stock assessment working group.
Therefore a fractional factorial design in which some of the possible combinations are omitted may be prefered.

However, when conducting a Management Strategy Evaluation (MSE, SCRS2013/35) a large number of scenarios need to be considered to
evaluate the main sources of uncertainties. I.e. the Operating Models (OM) will need to be 
conditioned on a wider range of data and knowledge that routinely considered within a stock assessment. 

In other words while only a few scenarios are routinely be considered within an ICCAT stock assessment, many more 
scenarios will need to be run as part of an MSE. This presents a potential problem if
the Scenarios from an MSE result in different conclusions from those ran in a stock assessment.

We therefore first specify a base case and then factors with levels that represent the main uncertainties. In the
stock assessment WG the main effects can be evaluated by varying 1 factor at a time. Hopefully this will 
allow the stock assessment to \textit{bracket} the main uncertainty and act as a simple screening experiment, 
to determine the factors have the greatest influence on the perception of stock dynamics.
Based on the identification of the most important factors, a multi-level designed experiment can then be developed
for the MSE that includes interactions between factors.

Choice and/or weighting of scenarios depends on plausibility.

Scenarios will be based on a base case (\textbf{BC}) and a factorial design with several \textbf{factors} each with a number of discrete \textbf{levels}
large number of scenarios will need to be considered for the \textbf{OM}, \textbf{OEM} and \textbf{MP} to evaluate the main sources of uncertainties. 
Due to the potentially large number of combinations a fractional factorial design in which only some of the possible combinations are run may be prefered.
Choice and weighting of scenarios depends on plausibility.

\subsection{Operating Model}\label{om}

The base case is given in \textbf{table} \ref{tab:bc} and the scenarions to be considered in \textbf{table} \ref{tab:om}.
There are eight factors i.e. aasumed natural mortality and maturitity ogives, CPUE series considered, long line selectivity shape, penalty on recruit deviations used, catch-at-size
(CAS) included in the fit, assumed sample sizes for the CAS and whether tagging data were used when fitting.    

\subsection{Observation Error Model}\label{oem}

The scenarions considered are given in \textbf{table} \ref{tab:oem}

\subsection{Management Procedure}\label{mp}

The MPs are based on \gls{aspic} and the scenarions considered are given in \textbf{table} \ref{tab:mp}


\subsection{Scenarios}
It is impractical tot run them all, but by adding stochastic noise to each of the  25509168 combinations it is possible to look at the main effects and lower 
order iteractions, (i.e. 1,2,3,4) using a bayesian belief network.

The benefit is that you can run a large number of lower order interactions, the downside is that you cant look at all interactions. But is you were to try and run 1000 for each comination you couldnt
anyway.

\section{Discussion}\label{discussion}

  \section{Conclusions}\label{conclusions	}


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\newpage\clearpage\section{Tables}


\begin{table}
\begin{center}
\label{tab:datasumm}
\begin{tabular}{|cccc|}
\hline
{\tiny Factor} & {\tiny Values} & {\tiny Notes} & {\tiny References} \\
\hline\hline
{\tiny $M_0$} 			& {\tiny 0.3 for all ages}     					& {\tiny As assumed in 2011} 	& {\tiny }\\
{\tiny $Maturity$} 		& {\tiny 0,0,0,0,.5,1,...}     					& {\tiny ''}			& {\tiny }\\
{\tiny CPUE} 			& {\tiny All CPUE Series}      					& {\tiny ''}			& {\tiny }\\
{\tiny LL Selectivities}	& {\tiny 5, 8, 9, 10 \& 11 logistic. Others domeshaped}	& {\tiny ''}			& {\tiny }\\
{\tiny Penalty on recruit devs}	& {\tiny 20 }               					& {\tiny ''}			& {\tiny }\\
{\tiny CAS} 			& {\tiny Include China-Taipei} 					& {\tiny ''}			& {\tiny }\\
{\tiny Sample size} 		& {\tiny Equal weights}        					& {\tiny ''}			& {\tiny }\\
{\tiny Tagging data} 		& {\tiny None}                 					& {\tiny ''}			& {\tiny }\\
\hline
\end{tabular}
\end{center}
\caption{Base Case options}
\label{tab:bc}
\end{table}


\begin{table}
\begin{center}
\label{tab:datasumm}
\begin{tabular}{|cccccc|}
\hline
{\tiny Factor} & {\tiny Levels} & {\tiny $\Sigma N$} & {\tiny Values} & {\tiny Prior} & {\tiny Weighting}\\
\hline\hline
{\tiny $M_0$} 			& {\tiny 3}   & {\tiny 3}  	& {\tiny  BC; Lorezen; Chen \& Watanabe} 	          	& {\tiny ?}  	& {\tiny ?}\\
{\tiny $Maturity$} 		& {\tiny 2}   & {\tiny 6}  	& {\tiny  BC; 0,0,0,0.25,.5,.75,1}  				& {\tiny ?}  	& {\tiny ?}\\
{\tiny CPUE} 			& {\tiny 2}   & {\tiny 12} 	& {\tiny  BC; exclude Japan}     	         		& {\tiny ?}  	& {\tiny ?}\\
{\tiny LL Selectivities}	& {\tiny 2}   & {\tiny 24} 	& {\tiny  BC, free}		                               	& {\tiny ?}  	& {\tiny ?}\\
{\tiny Penalty on recruit devs}	& {\tiny 2}   & {\tiny 48} 	& {\tiny  BC; 10}		                              	& {\tiny ?}  	& {\tiny ?}\\
{\tiny CAS} 			& {\tiny 3}   & {\tiny 144} 	& {\tiny  BC; ex	clude C-T; drop all}		              	& {\tiny ?}  	& {\tiny ?}\\
{\tiny Sample size} 		& {\tiny 2}   & {\tiny 288} 	& {\tiny  BC; 1-7 divided by 10, others by 1000}  		& {\tiny ?}  	& {\tiny ?}\\
{\tiny Tagging data} 		& {\tiny 2}   & {\tiny 576} 	& {\tiny  BC; Include}                           		& {\tiny ?}  	& {\tiny ?}\\
\hline
\end{tabular}
\end{center}
\caption{OM options}
\label{tab:om}
\end{table}

\begin{table}
\begin{center}
\label{tab:datasumm}
\begin{tabular}{|cccccc|}
\hline
{\tiny Factor} & {\tiny Levels} & {\tiny $\Sigma N$} & {\tiny Values} & {\tiny Prior} & {\tiny Weighting}\\
\hline\hline
{\tiny  Catch $\sigma$}		& {\tiny 3}  {\tiny 0.2,0.3,0.4	}	& {\tiny  3}  	& {\tiny  }  	& {\tiny ?}  	& {\tiny ?}\\
{\tiny  CPUE  $\sigma$} 	& {\tiny 3}  {\tiny 0.2,0.3,0.4}	& {\tiny  9} 	& {\tiny  } 	& {\tiny ?}  	& {\tiny ?}\\
{\tiny  CPUE  $\omega$} 	& {\tiny 2}  {\tiny 0.5, 1, 2} 		& {\tiny  18} 	& {\tiny  } 	& {\tiny ?}  	& {\tiny ?}\\
{\tiny  CPUE  age range} 	& {\tiny 3}  {\tiny all, adults} 	& {\tiny  54} 	& {\tiny  } 	& {\tiny ?}  	& {\tiny ?}\\
\hline
\end{tabular}
\end{center}
\caption{OEM options}
\label{tab:oem}
\end{table}


\begin{table}
\begin{center}
\label{tab:datasumm}
\begin{tabular}{|cccccc|}
\hline
{\tiny Factor} & {\tiny Levels} & {\tiny $\Sigma N$} & {\tiny Values} & {\tiny Prior} & {\tiny Weighting}\\
\hline\hline
{\tiny $r$} 	 				& {\tiny 3}  	& {\tiny 3} 	& {\tiny estimate; prior, perfect}	& {\tiny ?}    & {\tiny ?}\\
{\tiny $K$}					& {\tiny 3}  	& {\tiny 9}  	& {\tiny estimate; prior, perfect} 	& {\tiny ?}    & {\tiny ?}\\
{\tiny Shape} 					& {\tiny 3}  	& {\tiny 27} 	& {\tiny fix; prior, perfect}      	& {\tiny ?}    & {\tiny ?}\\
{\tiny $B_{target}$ as \% of $F_{MSY}$} 	& {\tiny 3}  	& {\tiny 81} 	& {\tiny 60\%,75\%,90\%} 		& {\tiny ?}    & {\tiny ?}\\
{\tiny $B_{lim}$ as \% of $B_{MSY}$}		& {\tiny 3}  	& {\tiny 243} 	& {\tiny 30\%,35\%,45\%} 	       	& {\tiny ?}    & {\tiny ?}\\
{\tiny $B_{lim}$ as \% of $K$}			& {\tiny 3}  	& {\tiny 729} 	& {\tiny 15\%,20\%,25\%}         	& {\tiny ?}    & {\tiny ?}\\
{\tiny $B_{Theshold}$ as \% of $B_{MSY}$}	& {\tiny 3}  	& {\tiny 2187} 	& {\tiny 70\%,85\%,100\%} 		& {\tiny ?}    & {\tiny ?}\\
{\tiny $B_{Theshold}$ as \% of $K$}		& {\tiny 3}  	& {\tiny 6561}	& {\tiny 35\%,40\%,50\%} 		& {\tiny ?}    & {\tiny ?}\\
\hline
\end{tabular}
\end{center}
\caption{MP options}
\label{tab:mp}
\end{table}


\newpage\clearpage\section{Figures}

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